Reciprocal Lattice: Visible Points in an X-Ray Experiment

In summary: This is a reprint of an article from 1985 about a computer code for calculating Umwegs. Very technical, but it covers the basics.
  • #1
Dr_Pill
41
0
I got a bunch of questions about reciprocal lattice, I start with this one:

In an x-ray experiment:

For one specific orientation of your incident beam on your real lattice, only a portion of the points of your reciprocal lattice will become visible as your diffraction pattern right?

See my picture

nm4bBeB.jpg


For one incident beam, only the parallel planes are involved in your diffraction and so only the reciprocal lattice points that represent these set of parallel planes will becoem visible on your diffraction pattern

If you want to make other reciprocal points points visible on your diffraction pattern, u have to change the orientation of your incident beam so that another set of parallel planes is involved in diffraction
So in first picture, your blue beam will get the reciprocal points that representing the green parallel planes visible on your diffraction pattern.

Second picture, the same blue beam does nothing on the purple planes, so the reciprocal points that represents the purple planes will not be visible on the diffraction pattern.

Is this correct?
 
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  • #2
It might help with the Forum formatting if you reduce the size of your image to no more than 800 pixels by 600 pixels. There's no reason for it to be THIS big.

Zz.
 
  • #3
ZapperZ said:
It might help with the Forum formatting if you reduce the size of your image to no more than 800 pixels by 600 pixels. There's no reason for it to be THIS big.

Zz.

Ok, like this? But now my picture is unsharp.
 
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  • #4
Dr_Pill said:
how can i resize it?

Remove the image, and upload a new, resized version.

Zz.
 
  • #5
Dr. Pill,

your images are in real space, not reciprocal space.

It is perfectly possible to align a single crystal such that two or even three sets of lattice planes fulfull the Bragg condition simultaneously.

For the two-beam case this can be done by aligning one Bragg peak (corresponding to the reciprocal space vector Q), and by then rotating the crystal about the vector Q until you excite a second reflection (=changing the azimuthal angle). To get 3 simultaneous reflections you also need to tune the photon energy just right.

The effect is known by several names including "Umweganregung", "Renninger effect" and "Multiple beam diffracton". It was first described in 1935.

The following links give a bit more informaiton:

P. P. Ewald, Rev. Mod. Phys. v37, pp46 (1965)
http://rmp.aps.org/abstract/RMP/v37/i1/p46_1
This is an excellent review article about the early theory of x-ray diffraction, written by one of the founding fathers. Highly recommended if you are interested in x-rays.

Renninger, Z. Phys v. 106 pp 141 (1937) in German
http://link.springer.com/article/10.1007/BF01340315

Description of a computer code for calculating Umwegs.
http://www1.uni-hamburg.de/mpi/rossmanith/Reprints/Z_Krist_85.pdf
 

1. What is a reciprocal lattice?

A reciprocal lattice is a mathematical concept used in crystallography to describe the arrangement of atoms in a crystal. It is a representation of the inverse of the crystal lattice, with points in the reciprocal lattice corresponding to planes in the crystal lattice.

2. How is the reciprocal lattice related to an X-ray experiment?

In an X-ray experiment, a beam of X-rays is directed at a crystal, and the scattered X-rays create an interference pattern. The positions of the bright spots in this pattern correspond to the points in the reciprocal lattice that are visible in the experiment.

3. What is the significance of the visible points in an X-ray experiment?

The visible points in an X-ray experiment represent the planes in the crystal lattice that are oriented in such a way that they diffract the X-rays to create the observed interference pattern. By studying the positions and intensities of these points, scientists can determine the crystal structure and properties of the material being studied.

4. How do you calculate the reciprocal lattice vectors?

The reciprocal lattice vectors can be calculated using the Bragg's law, which relates the wavelength of the incident X-rays to the spacing between crystal planes. The reciprocal lattice vectors are perpendicular to the crystal planes and their lengths are inversely proportional to the spacing between the planes.

5. Can the reciprocal lattice be used to study other materials besides crystals?

Yes, the concept of reciprocal lattice can also be applied to other periodic structures, such as quasicrystals and photonic crystals. In these cases, the reciprocal lattice can provide valuable information about the arrangement of atoms or other components in the material, and can aid in the design of new materials with desired properties.

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